8 Solving systems of linear equations[1].doc

Solving systems of linear equations1. z+w3=k6z10w=8Consider the system of equations above, where k is a constant. For which value of k are there infinitely many (w, z) solutions?A. -195B. 5C. 8D. None of the aboveCorrect answer: D Difficulty level: 22. 5x4y=2a4x5y=2Which of the following choices of a will result in a system of linear equations with exactly one solution?A. a can be any numberB. a can be any number except 0.8C. a can be any number except 0.8D. a = 0.8Correct answer: A Difficulty level: 23. 12x+23-1=2y+13-13 x-2-4y+12=-2Consider the system of equations above. Which of the following statements about this system is true?A. There is only one (x, y) solution and x+y is positive.B. There is only one (x, y) solution and x+y is negative.C. There are infinitely many (x, y) solutions.D. There are no (x, y) solutions.Correct answer: C Difficulty level: 24. 23x+1-45y=13 25x+132y+1=15Consider the system of equations above. Which of the following statements is true?A. There is only one solution (x, y) and x+y is positive.B. There is only one solution (x, y) and x+y is negative.C. There are infinitely many solutions.D. There are no solutions.Correct answer: B Difficulty level: 25. 1.70p0.34q=00.17(q+1)0.85(p1)=0Consider the system of equations above. How many (p, q) solutions does this system have?A. 0B. 1C. Infinitely manyD. None of the aboveCorrect answer: A Difficulty level: 26. 3s+2t3=c 7s5t =4Consider the system of equations above, where c is a constant. For which value of c is there exactly one (s, t) solution where s=1?A. -4.8B. 447C. 18D. None of the aboveCorrect answer: A Difficulty level: 27. 0.7a0.8b=0.1a1.4=6(b0.1)Consider the system of equations above. If (a, b) is the solution to the system, then what is the value of the sum of a and b?A. -0.5B. -0.1C. 0.1D. 0.5Correct answer: D Difficulty level: 28. 6(1a) =3(ab)+14(b2) =3aConsider the system of equations above. If (a, b) is the solution to the system, then what is the value of a-b?A. -1,276243B. 299C. 4427D. 1,276243Correct answer: D Difficulty level: 29. 7p=9(p+q)+119q+3=4(7q+p)Consider the system of equations above. If (p, q) is the solution to the system, then what is the value of p+q?Correct answer: -9 Difficulty level: 210. 0.2x+by=7.25.6x0.8y=4Consider the system of equations above. For what value of b will the system have exactly one solution(x,y) with x=2? Round the answer to the nearest tenth.Correct answer: 0.8 Difficulty level: 311. 4a5b4=212b+5a11=9Consider the system of equations above. What is the value of 2ab?A. -5B. -13C. 13D. 5Correct answer: A Difficulty level: 312. 2x1=y 3x1 =yConsider the system of equations above. Which of the following statements about this system is true?A. There is only one (x, y) solution and y is positive.B. There is only one (x, y) solution and y is negative.C. There are infinitely many (x, y) solutions.D. There are no (x, y) solutions.Correct answer: B Difficulty level: 313. ay2-32x+1=43y-12x+56 56y-56x+52=0Consider the system of equations above, where a is a constant. For which value of a is (x, y)=(4, 1) a solution?A. -3427B. -127C. 349D. None of the aboveCorrect answer: D Difficulty level: 314. 44(j+2k) =1222k=11j+16Consider the system of equations above. How many solutions (j,k) does this system have?A. 0B. Exactly 1C. Exactly 2D. Infinitely manyCorrect answer: A Difficulty level: 315. 1.5a4.5b=3(a+b)5.5b=5(ba)+2.5aConsider the system of equations above. If (a, b) is the solution to the system, then what is the value of ba?Correct answer: 0 Difficulty level: 316. 5x2y=610x4y=cWhich of the following choices of c will result in a system of linear equations with no solutions?A. c=12B. c can be any number other than 12C. c can be any number other than 12D. c can be any numberCorrect answer: C Difficulty level: 317. x=6y7x6y=kConsider the system of equations above. Which of the following choices of k will result in a system of equations with infinitely many solutions?A. Any numberB. Any number except 7C. 7D. -7Correct answer: C Difficulty level: 318. 65p+kq=45 q=35p-25Consider the system of equations above, where k is a constant. For which value of k is there no (p, q) solutions?A. -2B. 0C. 2D. None of the aboveCorrect answer: D Difficulty level: 419. 11y=6(z+1)13y4y24=c(z1)For what value of c does the above system of linear equations in the variables y and z have infinitely many solutions?Correct answer: 12 Difficulty level: 420. 2x-13-32y-16=0 3y-12+83x-16=0Consider the system of equations above. If (x, y) is the solution to the system, then what is the value of the sum of x and y?A. 56B. 2536C. 23D. None of the aboveCorrect answer: B Difficulty level: 421. 5.1x+3y=1.23.2x8y=bWhich of the following choices of b will result in a system of linear equations with exactly one solution?A. b can be any numberB. b can be any number except 1.2C. b can be any number except 1.2D. b=1.2Correct answer: A Difficulty level: 422. 0.6=1.5(a+c(b+0.8)0.2=2.5(b0.4(1.21.5a)Consider the system of equations above, where c is a constant. For which value of ccc are there no (a, b) solutions?A. 0B. 517C. 53D. None of the aboveCorrect answer: C Difficulty level: 423. a(pq) =1p = 2q1Consider the system of equations above, where a is a constant. For which value of a is (p, q)=(1, 1) a solution?A. 0B. 1C. 2D. None of the aboveCorrect answer: D Difficulty level: 424. ay-13+x2=0 3y-x-1=0Consider the system of equations above, where a is a constant. For which value of a are there infinitely many (x, y) solutions?A. -32B. 56C. 3D. None of the aboveCorrect answer: A Difficulty level: 425. ay=2x+1y=2x+2Consider the system of equations above, where a is a constant. For what value of a are there no (x, y) solutions?Correct answer: 1 D